Question

Consider the function y=x/(x+1)

a) Find dy/dx

b) Find the equation of the line tangent to the curve at x=-2

c) Find the equation of the line normal to the curve at x=1

Answer 1

dy/dx = [(x+1)1 -x(1) ] / (x+1)^2

= 1/(x+1)^2

at x = -2
y = -2/-1 = 2 so through point (-2,2)
dy/dx = m = 1/1 = 1
so
y = 1 x + b
2 = -2 + b
b = 4
y = x +
for part c
find a new m at x = 1, y = 1/2
the m we want = -1/m
then repeat method of part b